Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

For R b < r < R c , we have∆µ p (r) = ze2r − 2 3 πe2 ρ e (3R 2 c −r2 ).The energy contribution from outside the inner cell is given by(D.12)E C,o = −πzρ e e 2 (Rc 2 4π2−R2 b )+15 ρ2 e (4R5 c −5R2 c R3 b +R5 b ). (D.13)For energy minimization, we have∫ ( ∫F = E tot −λ 1 (ρ n +ρ p )d 3 r − 4π (3 R3 cρ)−λ ∫ 2 ρ p d 3 r − 4π )3 R3 cρY eI chose unknowns with ρ n , ρ p , Y e , µ n,0 , and µ p,0 then we have equations to solve(D.14)0 = F 0,N : µ n (ρ n ,ρ p )−µ n,0 = 00 = F N+1,2N+1 : µ p (ρ n ,ρ p )−µ p,0 = 0∫0 = F 2N+2 : (ρ n +ρ p )d 3 r − 4 3 πR3 c ρ = 0∫0 = F 2N+3 : ρ p d 3 r − 4 3 πR3 cρY e = 0(D.15)0 = F 2N+4 : µ n,0 −µ p,0 −µ e (Y e ) = 0In the lower density ( ρ < 0.01/fm 3 ) region, two methods give almost same result. Asdensity increases, the uniform electron density approximation is unstable numerically inFRTF model.126